{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T03:12:05Z","timestamp":1767237125236},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2013,9,26]],"date-time":"2013-09-26T00:00:00Z","timestamp":1380153600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2015,3]]},"DOI":"10.1007\/s10623-013-9881-9","type":"journal-article","created":{"date-parts":[[2013,9,25]],"date-time":"2013-09-25T15:09:55Z","timestamp":1380121795000},"page":"581-600","source":"Crossref","is-referenced-by-count":1,"title":["Paley type sets from cyclotomic classes and Arasu\u2013Dillon\u2013Player difference sets"],"prefix":"10.1007","volume":"74","author":[{"given":"Yu Qing","family":"Chen","sequence":"first","affiliation":[]},{"given":"Tao","family":"Feng","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,9,26]]},"reference":[{"key":"9881_CR1","unstructured":"Arasu K.T.: Sequences and arrays with desirable correlation properties. http:\/\/www.math.uniri.hr\/NATO-ASI\/abstracts\/arasu.pdf ."},{"key":"9881_CR2","unstructured":"Arasu K.T.: A reduction theorem for circulant weighing matrices. Australas. J. Comb. 18, 111\u2013114 (1998)."},{"key":"9881_CR3","doi-asserted-by":"crossref","unstructured":"Arasu K.T., Chen Y.Q., Dillon J.F., Liu X., Player K.J.: Abelian difference sets of order n dividing $$\\lambda $$ \u03bb . Des. Codes Cryptogr. 44, 307\u2013319 (2007).","DOI":"10.1007\/s10623-007-9102-5"},{"key":"9881_CR4","unstructured":"Arasu K.T., Dillon J.F., Player K.J.: Character sum factorizations yield perfect sequences (in press)."},{"key":"9881_CR5","doi-asserted-by":"crossref","unstructured":"Arasu K.T., Leung K.H., Ma S.L., Nabavi A., Ray-Chaudhuri D.K.: Determination of all possible orders of weight 16 circulant weighing matrices. Finite Fields Appl. 12, 498\u2013538 (2006).","DOI":"10.1016\/j.ffa.2005.06.009"},{"key":"9881_CR6","doi-asserted-by":"crossref","unstructured":"Arasu K.T., Leung K.H., Ma S.L., Nabavi A., Ray-Chaudhuri D.K.: Circulant weighing matrices of weight $$2^{2t}$$ 2 2 t . Des. Codes Cryptogr. 41, 111\u2013123 (2006).","DOI":"10.1007\/s10623-006-0026-2"},{"key":"9881_CR7","doi-asserted-by":"crossref","unstructured":"Arasu K.T., Ma S.L.: Some new results on circulant weighing matrices. J. Algebraic Comb. 14, 91\u2013101 (2001).","DOI":"10.1023\/A:1011903510338"},{"key":"9881_CR8","unstructured":"Berndt B.C., Evans R.J., Williams K.S.: Gauss and Jacobi Sums, Canadian Mathematical Society Series of Monographs and Advanced Texts. Wiley, New York (1998)."},{"key":"9881_CR9","unstructured":"Beth T., Jungnickel D., Lenz H.: Design Theory, vol. 1, 2nd edn. Cambridge University Press, Cambridge (1999)."},{"key":"9881_CR10","doi-asserted-by":"crossref","unstructured":"Carlitz L.: A theorem on permutations in a finite field. Proc. Am. Math. Soc. 11, 456\u2013459 (1960).","DOI":"10.2307\/2034798"},{"key":"9881_CR11","doi-asserted-by":"crossref","unstructured":"Camion P., Mann H.B.: Antisymmetric difference sets. J. Number Theory 4, 266\u2013268 (1972).","DOI":"10.1016\/0022-314X(72)90053-4"},{"key":"9881_CR12","doi-asserted-by":"crossref","unstructured":"Chen Y.Q.: On the existence of abelian Hadamard difference sets and a new family of difference sets. Finite Fields Appl. 3, 234\u2013256 (1997).","DOI":"10.1006\/ffta.1997.0184"},{"key":"9881_CR13","unstructured":"Chen Y.Q.: Multiplicative characterization of some difference sets in elementary abelian groups. J. Comb. Inf. Syst. Sci. 34, 95\u2013111 (2009)."},{"key":"9881_CR14","unstructured":"Chen Y.Q.: Divisible designs and semi-regular relative difference sets from additive Hadamard cocycles. J. Comb. Theory Ser. A 118, 2185\u20132206 (2011)."},{"key":"9881_CR15","doi-asserted-by":"crossref","unstructured":"Chen Y.Q., Feng T.: Abelian and non-abelian Paley type group schemes. Des. Codes Cryptogr. 68, 141\u2013154 (2013).","DOI":"10.1007\/s10623-012-9640-3"},{"key":"9881_CR16","unstructured":"Chen Y.Q., Polhill J.: Paley type group schemes and planar Dembowski\u2013Ostrom polynomials. Discret. Math. 311, 1349\u20131364 (2011)."},{"key":"9881_CR17","doi-asserted-by":"crossref","unstructured":"Chen Y.Q., Xiang Q., Sehgal S.K.: An exponent bound on skew Hadamard abelian difference sets. Des. Codes Cryptogr. 4, 313\u2013317 (1994).","DOI":"10.1007\/BF01388647"},{"key":"9881_CR18","unstructured":"Coulter R., Kosick P.: Commutative semifields of order 243 and 3125. Finite Fields Theory appl. Contemp. Math. 518, 129\u2013136 (2010)."},{"key":"9881_CR19","doi-asserted-by":"crossref","unstructured":"Davis J.A.: Partial difference sets in p-groups. Arch. Math. 63, 103\u2013110 (1994).","DOI":"10.1007\/BF01189882"},{"key":"9881_CR20","unstructured":"Dillon J.F.: Elementary Hadamard difference sets. Ph.D. thesis, University of Maryland (1974)."},{"key":"9881_CR21","unstructured":"Dillon J.F.: Elementary Hadamard difference sets. In: Proceedings of the Sixth Southeastern Conference on Combinatorics, Graph Theory, and Computing (1975), pp. 237\u2013249. Congressus Numerantium, No. XIV, Utilitas Math., Winnipeg, Manitoba (1975)."},{"key":"9881_CR22","doi-asserted-by":"crossref","unstructured":"Dillon J.F.: Multiplicative difference sets via additive characters. Des. Codes Croptogr. 17, 225\u2013235 (1999).","DOI":"10.1023\/A:1026435428030"},{"key":"9881_CR23","unstructured":"Ding C., Wang Z., Xiang Q.: Skew Hadamard difference sets from the Ree\u2013Tits slice sympletic spreads in PG $$(3,3^{2h+1})$$ ( 3 , 3 2 h + 1 ) . J. Comb. Theory Ser. A 114, 867\u2013887 (2007)."},{"key":"9881_CR24","unstructured":"Ding C., Yin J.: A family of skew Hadamard difference sets. J. Comb. Theory Ser. A 113, 1526\u20131535 (2006)."},{"key":"9881_CR25","unstructured":"Feng T.: Non-abelian skew Hadamard difference sets fixed by a prescribed automorphism. J. Comb. Theory Ser. A 118, 27\u201336 (2011)."},{"key":"9881_CR26","unstructured":"Feng T., Momihara K., Xiang Q.: Constructions of strongly regular Cayley graphs and skew Hadamard difference sets from cyclotomic classes, arXiv:1206.3354."},{"key":"9881_CR27","unstructured":"Feng T., Xiang Q.: Cyclotomic constructions of skew Hadamard difference sets. J. Comb. Theory Ser. A 119, 245\u2013256 (2012)."},{"key":"9881_CR28","unstructured":"Gordon B., Mills W.H., Welch L.R.: Some new difference sets. Can. J. Math. 14, 614\u2013625 (1962)."},{"key":"9881_CR29","doi-asserted-by":"crossref","unstructured":"Johnson E.C.: Skew-Hadamard abelian group difference sets. J. Algebra 4, 388\u2013402 (1966).","DOI":"10.1016\/0021-8693(66)90029-9"},{"key":"9881_CR30","doi-asserted-by":"crossref","unstructured":"Kantor W.M.: 2-Transitive symmetric designs. Trans. Am. Math. Soc. 146, 1\u201328 (1969).","DOI":"10.2307\/1995157"},{"key":"9881_CR31","doi-asserted-by":"crossref","unstructured":"Langevin P.: Calcus de certaines sommes de Gauss. J. Number Theory 63, 59\u201364 (1997).","DOI":"10.1006\/jnth.1997.2078"},{"key":"9881_CR32","unstructured":"Leung K.H., Ma S.L., Schmidt B.: Constructions of relative difference sets with classical parameters and circulant weighing matrices. J. Comb. Theory Ser. A 99, 111\u2013127 (2002)."},{"key":"9881_CR33","doi-asserted-by":"crossref","unstructured":"Lubotzky A., Phillips R., Sarnak P.: Ramanujan graphs. Combinatorica 8, 261\u2013277 (1988).","DOI":"10.1007\/BF02126799"},{"key":"9881_CR34","unstructured":"Ma S.L.: Partial difference sets. Discret. Math. 52, 75\u201389 (1984)."},{"key":"9881_CR35","unstructured":"Ma S.L.: Polynomial addition sets and symmetric difference sets. In: Ray-Chandhuri, D. (ed.) Coding Theory and Design Theory Part II: Design Theory, pp. 273\u2013279. Springer, New York (1990)."},{"key":"9881_CR36","doi-asserted-by":"crossref","unstructured":"Ma S.L.: A survey of partial difference sets. Des. Codes Cryptogr. 4, 221\u2013261 (1994).","DOI":"10.1007\/BF01388454"},{"key":"9881_CR37","doi-asserted-by":"crossref","unstructured":"Ma S.L.: Reversible relative difference sets. Combinatorica 12, 425\u2013432 (1992).","DOI":"10.1007\/BF01305235"},{"key":"9881_CR38","unstructured":"Momihara K.: Skew Hadamard difference sets from cyclotomic strongly regular graphs. arXiv:1211. 2864v1."},{"key":"9881_CR39","unstructured":"Muzychuk M.: On skew Hadamard difference sets. arXiv:1012.2089v1."},{"key":"9881_CR40","doi-asserted-by":"crossref","unstructured":"Paley R.E.A.C.: On orthogonal matrices. J. Math. Phys. 12, 311\u2013320 (1933).","DOI":"10.1002\/sapm1933121311"},{"key":"9881_CR41","doi-asserted-by":"crossref","unstructured":"Peisert W.: All self-complementary symmetric graphs. J. Algebra 240, 209\u2013229 (2001).","DOI":"10.1006\/jabr.2000.8714"},{"key":"9881_CR42","doi-asserted-by":"crossref","unstructured":"Polhill J.: Paley type partial difference sets in non $$p$$ p -groups. Des. Codes Cryptogr. 52, 163\u2013169 (2009).","DOI":"10.1007\/s10623-009-9274-2"},{"key":"9881_CR43","unstructured":"Polhill J.: Paley type partial difference sets in groups of order $$n^4$$ n 4 and $$9n^4$$ 9 n 4 for any odd $$n$$ n . J. Comb. Theory Ser. A 117, 1027\u20131036 (2010)."},{"key":"9881_CR44","doi-asserted-by":"crossref","unstructured":"Pott A.: Finite geometry and character theory. Lecture Notes in Mathematics, vol. 1601. Springer, Berlin, (1995).","DOI":"10.1007\/BFb0094449"},{"key":"9881_CR45","doi-asserted-by":"crossref","unstructured":"Weng G., Qiu W., Wang Z., Xiang Q.: Pseudo-Paley graphs and skew Hadamard difference sets from presemifields. Des. Codes Cryptogr. 44, 49\u201362 (2007).","DOI":"10.1007\/s10623-007-9057-6"},{"key":"9881_CR46","unstructured":"Xiang Q.: Note on Paley type partial difference sets. Groups, Difference Sets, and the Monster (Columbus, OH, 1993), pp. 239\u2013244. Ohio State University Mathematical Research Institute Publications, Berlin (1996)."},{"key":"9881_CR47","unstructured":"Yamamoto K.: On congruences arising from relative Gauss sum. Number Theory and Combinatorics, pp. 423\u2013446. World Scientific, Singapore (1955)."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-013-9881-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10623-013-9881-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-013-9881-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,25]],"date-time":"2019-07-25T13:44:03Z","timestamp":1564062243000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10623-013-9881-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9,26]]},"references-count":47,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,3]]}},"alternative-id":["9881"],"URL":"https:\/\/doi.org\/10.1007\/s10623-013-9881-9","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,9,26]]}}}